# Performance Evaluation and Active Portfolio Management

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Performance Evaluation and Active Portfolio Management
Chapter 24 Performance Evaluation and Active Portfolio Management

Introduction Complicated subject
Theoretically correct measures are difficult to construct Different statistics or measures are appropriate for different types of investment decisions or portfolios Many industry and academic measures are different The nature of active managements leads to measurement problems

Abnormal Performance What is abnormal?
Abnormal performance is measured: Benchmark portfolio Market adjusted Market model / index model adjusted Reward to risk measures such as the Sharpe Measure: E (rp-rf) / sp

Factors That Lead to Abnormal Performance
Market timing Superior selection Sectors or industries Individual companies

1) Sharpe Index rp - rf p s rp = Average return on the portfolio rf = Average risk free rate p = Standard deviation of portfolio return s

2) Treynor Measure rp - rf ßp rp = Average return on the portfolio rf = Average risk free rate ßp = Weighted average b for portfolio

3) Jensen’s Measure = rp - [ rf + ßp ( rm - rf) ] a p = Alpha for the portfolio a p rp = Average return on the portfolio ßp = Weighted average Beta rf = Average risk free rate rm = Avg. return on market index port.

M2 Measure Developed by Modigliani and Modigliani
Equates the volatility of the managed portfolio with the market by creating a hypothetical portfolio made up of T-bills and the managed portfolio If the risk is lower than the market, leverage is used and the hypothetical portfolio is compared to the market

M2 Measure: Example Managed Portfolio Market T-bill Return 35% 28% 6%
Stan. Dev 42% % % Hypothetical Portfolio: Same Risk as Market 30/42 = .714 in P (1-.714) or .286 in T-bills (.714) (.35) + (.286) (.06) = 26.7% Since this return is less than the market, the managed portfolio underperformed

T2 (Treynor Square) Measure
Used to convert the Treynor Measure into percentage return basis Makes it easier to interpret and compare Equates the beta of the managed portfolio with the market’s beta of 1 by creating a hypothetical portfolio made up of T-bills and the managed portfolio If the beta is lower than one, leverage is used and the hypothetical portfolio is compared to the market

T2 Example Port. P. Market Risk Prem. (r-rf) 18% 15% Beta 0.80 1.0
Alpha % 0% Treynor Measure Risk Free rate 5% T2P = (RP – rf)/Bp – (RM – rf) =13/.8 – 10 = 6.25%

Which Measure is Appropriate?
It depends on investment assumptions 1) If the portfolio represents the entire investment for an individual, Sharpe Index compared to the Sharpe Index for the market. 2) If many alternatives are possible, use the Jensen a or the Treynor measure The Treynor measure is more complete because it adjusts for risk

Limitations Assumptions underlying measures limit their usefulness
When the portfolio is being actively managed, basic stability requirements are not met Practitioners often use benchmark portfolio comparisons to measure performance

Decomposing overall performance into components Components are related to specific elements of performance Example components Broad Allocation Industry Security Choice Up and Down Markets

Process of Attributing Performance to Components
Set up a ‘Benchmark’ or ‘Bogey’ portfolio Use indexes for each component Use target weight structure

Appropriate Benchmark
Unambiguous – anyone can reproduce it Investable Measurable Specified in Advance

Process of Attributing Performance to Components
Calculate the return on the ‘Bogey’ and on the managed portfolio Explain the difference in return based on component weights or selection Summarize the performance differences into appropriate categories

See Example

Lure of Active Management
Are markets totally efficient? Some managers outperform the market for extended periods While the abnormal performance may not be too large, it is too large to be attributed solely to noise Evidence of anomalies such as the turn of the year exist The evidence suggests that there is some role for active management 2

Market Timing Adjust the portfolio for movements in the market
Shift between stocks and money market instruments or bonds Results: higher returns, lower risk (downside is eliminated) With perfect ability to forecast behaves like an option 3

Style Analysis Introduced by Bill Sharpe
Explaining percentage returns by allocation to style Style Analysis has become popular with the industry

Similar to mean Standard Deviation rankings Companies are put into peer groups Stars are assigned 1-lowest 5-highest Highly correlated to Sharpe measures

Superior Selection Ability
Concentrate funds in undervalued stocks or undervalued sectors or industries Balance funds in an active portfolio and in a passive portfolio Active selection will mean some unsystematic risk 8

Treynor-Black Model Model used to combine actively managed stocks with a passively managed portfolio Using a reward-to-risk measure that is similar to the the Sharpe Measure, the optimal combination of active and passive portfolios can be determined 9

Treynor-Black Model: Assumptions
Analysts will have a limited ability to find a select number of undervalued securities Portfolio managers can estimate the expected return and risk, and the abnormal performance for the actively-managed portfolio Portfolio managers can estimate the expected risk and return parameters for a broad market (passively managed) portfolio 10

Reward to Variability Measures
Appraisal Ratio =  A/eA a = Alpha for the active portfolio A s = Unsystematic standard deviation for active (eA) 12